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Fresh Groundwater Lens Development in Small Islands Under a Changing Climate

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Fresh Groundwater Lens Development in Small Islands Under a Changing Climate FRESH GROUNDWATER LENS DEVELOPMENT IN SMALL ISLANDS UNDER A CHANGING CLIMATE A Dissertation Presented to The Academic Faculty by Yuening Tang In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the School of Civil and Environmental Engineering Georgia Institute of Technology May 2021 COPYRIGHT © 2021 BY YUENING TANG FRESH GROUNDWATER LENS DEVELOPMENT IN SMALL ISLANDS UNDER A CHANGING CLIMATE Approved by: Dr. Jian Luo, Advisor Dr. Yi Deng School of Civil and Environmental School of Earth and Atmospheric Engineering Science Georgia Institute of Technology Georgia Institute of Technology Dr. Jingfeng Wang Dr. Chunhui Lu School of Civil and Environmental College of Water Conservancy and Engineering Hydropower Engineering Georgia Institute of Technology Hohai University Dr. Kevin A. Haas School of Civil and Environmental Engineering Georgia Institute of Technology Date Approved: May 2021 ACKNOWLEDGEMENTS I would like to express my deepest appreciation to my supervisor Dr. Jian Luo for his invaluable guidance and continuous support during my Ph.D. study. It’s extremely lucky and a great honor for me to have such a kind and knowledgeable supervisor in my Ph.D. career. His endless pursuit of knowledge and the patient yet serious attitude to student will enlighten my future career and be my lifetime fortune. My gratitude to Dr. Jian Luo would never come to an end. I would also like to thank my committee members: Dr. Jingfeng Wang, Dr. Kevin A. Haas, Dr. Yi Deng and Dr. Chunhui Lu for their constructive and insightful suggestions which help me to complete the thesis. I gratefully acknowledge the partial financial support from China Scholarship Council. My gratitude also goes to the colleagues in our office, Yue Zhao, Saubhagya Singh Rathore, Tongtong Xu for their help and advice to my research, and the friendship in my daily life. Finally, I would like to express sincerest gratitude to my parents: Xiaozhi Tang and Zhilan Tian for their unconditional support and love. They are always my strongest backing, which makes me fearless in regard of hardness. The sincerest gratitude extends to my boyfriend Yunlong Wang for his encouragement and company throughout my entire Ph. D career. iii TABLE OF CONTENTS ACKNOWLEDGEMENTS iii LIST OF TABLES vii LIST OF FIGURES viii LIST OF SYMBOLS AND ABBREVIATIONS xiv SUMMARY xvi CHAPTER 1. Introduction 1 1.1 Freshwater Lens in Small Islands 1 1.2 Research Motivation 4 1.3 Research Objective 6 1.4 Organization of This Thesis 8 CHAPTER 2. Literature Review 9 2.1 Freshwater Lens and Impact Factors 9 2.2 Mathematical Modeling 13 2.3 Laboratory and Field Observations 17 CHAPTER 3. Impact of Time-dependent Recharge on Fresh Groundwater Lens Development 20 3.1 Conceptual Model 20 3.2 Approximate Analytical Solution 21 3.2.1 Hantush Solution (1968) 21 3.2.2 Dimensional Analysis 25 3.2.3 Linear System Approach for Time-Dependent Recharge 26 3.3 Application 28 3.3.1 Periodic Recharge Function 29 3.3.2 Extended Drought Events 32 3.3.3 Random Time-series Recharge 33 3.4 Low-pass Filter Analysis 35 3.5 Conclusion 41 CHAPTER 4. Impact of Spatially Variable Recharge on Fresh Groundwater Lens Development 43 4.1 Conceptual Model 43 4.2 Mathematical Modeling 44 4.2.1 Governing Equation 44 4.2.2 Analytical Solution 46 4.2.3 Dimensional Analysis 47 4.2.4 Green’s Function Solution 48 4.2.5 Comparison with a Reported Analytical Solution 49 4.3 Application 50 iv 4.3.1 Concentrated Recharge at the Domain Center 50 4.3.2 Uncertainty Analysis of Randomly Distributed Recharge 52 4.4 Conclusion 56 CHAPTER 5. Critical Pumping Rate for Sustainable Use of Groundwater Lens 58 5.1 Conceptual Model 58 5.2 Approximate Analytical Solution 59 5.2.1 Groundwater Lens Interface Profile 59 5.2.2 Critical Pumping Rate 62 5.3 Conclusion 64 CHAPTER 6. Experimental Validation 66 6.1 Impact of Time-dependent Variable Recharge 66 6.2 Impact of Spatially Variable Recharge 67 6.3 Critical Pumping Rate 69 CHAPTER 7. Numerical Investigation 72 7.1 Impact of Time-dependent Variable Recharge 72 7.2 Impact of Spatially Variable Recharge 75 7.3 Critical Pumping Rate 78 7.3.1 Numerical Simulation 78 7.3.2 Effects of Recharge Rate and Well Penetration Depth 82 7.3.3 Effects of Hydraulic Conductivity 83 CHAPTER 8. Impact of Long-term Sea level Rise and Periodic Tide on Fresh Groundwater Lens Development 86 8.1 Conceptual Model 86 8.2 Numerical Simulation: Base Case 87 8.2.1 Numerical Setting 87 8.2.2 Comparison between the Long-term Sea Level Rise Case and Periodic Tide Case 90 8.2.3 Influence Zone 92 8.3 Sensitivity Analysis 93 8.3.1 Effect of Extent of Sea-level Rise 93 8.3.2 Effect of Recharge and Hydraulic Conductivity 95 8.4 Extent of Influence Zone 96 8.5 Multiple Seawater Intrusion Path 97 8.6 Conclusion 98 CHAPTER 9. Field Investigation for St. George Island 100 9.1 Impact of Time-dependent Recharge 101 9.2 Impact of Spatially Variable Recharge 103 9.3 Freshwater Critical Pumping Volume in St. George Island 105 9.4 Sea-level Rise 106 9.5 Summary 107 CHAPTER 10. Future Work 108 v 10.1 Future Work 108 10.1.1 Freshwater-seawater Mixing Zone 108 10.1.2 Development of Freshwater Lens in Heterogeneous Aquifer 108 10.1.3 Optimization of Multiple Wells in Small Islands 108 10.1.4 Circular Small Islands 109 10.1.5 Fully Bounded Rectangular Small Islands 109 10.1.6 Effect of Nonlinearity 109 10.1.7 Vertical Discharge in Freshwater Lens 110 10.2 Conclusions 111 REFERENCES 114 vi LIST OF TABLES Table 1. Fitted parameters for the second-order frequency response model. ................... 37 Table 2. Hydrogeologic and geometric parameters used in the numerical model for validating the approximate analytical solution ................................................................. 72 Table 3. Hydrogeologic and geometric parameters used in the numerical model for validating the analytical solution ...................................................................................... 77 Table 4. Hydrogeologic and geometric parameters used in the numerical model for validating the approximate analytical solution ................................................................. 80 Table 5. Hydrogeologic and geometric parameters used in the numerical model ............ 90 Table 6. Different combinations of hydraulic conductivity and recharge rate for Figure 35 ........................................................................................................................................... 96 vii LIST OF FIGURES Figure 1. Cross section of a symmetric freshwater lens structure in small strip islands. ... 2 Figure 2. Two-dimensional conceptual model for the groundwater lens under pumping at the center. ............................................................................................................................ 6 Figure 3. Sharp-interface based mathematical model of freshwater lens ......................... 13 Figure 4. Growth of groundwater lens thickness to the steady state at different locations on an island with the width 600m, hydraulic conductivity 10-3 m/s, recharge rate 10-7 m/s, and porosity 0.1. ................................................................................................................ 25 Figure 5. Dimensionless impulse response functions of squared lens thickness at different distances to the domain center in response to a unit impulse recharge function. x* = 0 represents the island center. .............................................................................................. 28 Figure 6. Groundwater lens shape and volume in response to periodic recharge. (a) Recharges with different cycle periods; (b) corresponding responses of the lens’s volume and thickness at the center. ............................................................................................... 31 Figure 7. Increasing normalized fluctuation versus T*. Fluctuations of 10%, 50% and 100% are corresponding to about T* = 200, 500 and 1300. .............................................. 31 Figure 8. Groundwater lens dimensionless volume (a) and thickness (b) for one month, six month and a constant average rainfall each year. ........................................................ 33 Figure 9. Groundwater lens volume corresponding to random time-series recharge. Dimensionless volume (a) and dimensionless thickness (b) for a random monthly recharge, the mean of 5000 realizations of random recharges, and a constant mean recharge; (c) the random monthly recharge over a period time of t* = 10000. ................ 35 viii Figure 10. Fitting of the physical model to the second-order system at the domain center (a) and edge (b). ................................................................................................................ 37 Figure 11. Bode plot of system frequency response. 1 dB = 20 log10|퐻(휔푓)| and −1 2휁(휔푓/휔푛) Phase = −tan ( 2). ....................................................................................... 38 1−(휔푓/휔푛) Figure 12. Periodic recharge with different cycle length and corresponding spectrum ... 40 Figure 13. Comparison between the derived analytical solution and a published steady- state analytical solution for two recharge rates. The domain is divided into two halves with the recharge rate ω1 and ω2, respectively. The ratio between ω2 and ω1 varies from 0 to 1. ................................................................................................................................... 50 Figure 14. Groundwater lens profile and volume for centralized, intensified recharge
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